; @origtpdbfilename ./TRS/higher-order/AProVE_HO/TakeDropWhile.trs
; @xtcfilename "./TRS_Standard/Applicative_05/TakeDropWhile.xml"
(format TRS)
(fun app 2)
(fun if 0)
(fun true 0)
(fun takeWhile 0)
(fun nil 0)
(fun cons 0)
(fun dropWhile 0)
(rule (app (app (app if true) x) y) x)
(rule (app (app (app if true) x) y) y)
(rule (app (app takeWhile p) nil) nil)
(rule (app (app takeWhile p) (app (app cons x) xs)) (app (app (app if (app p x)) (app (app cons x) (app (app takeWhile p) xs))) nil))
(rule (app (app dropWhile p) nil) nil)
(rule (app (app dropWhile p) (app (app cons x) xs)) (app (app (app if (app p x)) (app (app dropWhile p) xs)) (app (app cons x) xs)))